Concept explainers
(a)
The angle between the invar bars as a function of Celsius temperature.
(a)
Answer to Problem 31AP
The angle between the invar bars as a function of Celsius temperature is
Explanation of Solution
Given info: The distance between two holes drilled at
In the given diagram consider the right triangle that each invar bar makes with one half of the aluminum bar.
Then, the angle is,
Here,
Rearrange the above equation for
Conclusion:
Therefore, the angle between the invar bars as a function of Celsius temperature is
(b)
Whether the answer is accurate for negative as well as positive temperature or not.
(b)
Answer to Problem 31AP
Yes the answer is accurate for negative as well as positive temperature.
Explanation of Solution
Given info: The distance between two holes drilled at
If the temperature drops, the Celsius temperature becomes negative. The negative value of the Celsius temperature describes the contraction of the bars. So the answer is accurate for the negative temperature same as the positive temperature.
Conclusion:
Therefore, yes the answer is accurate for negative as well as positive temperature.
(c)
Whether the answer is accurate at
(c)
Answer to Problem 31AP
Yes, the answer is accurate at
Explanation of Solution
Given info: The distance between two holes drilled at
The expression for the angle between the invar bars is,
Substitute
The value of each angle of the right angle triangle is
Conclusion:
Therefore, Yes, the answer is accurate at
(d)
The angle between the invar bars and the aluminum bar as a function of Celsius temperature.
(d)
Answer to Problem 31AP
The angle between the invar bars and the aluminum bar as a function of Celsius temperature is
Explanation of Solution
Given info: The distance between two holes drilled at
In the given diagram consider the right triangle that each invar bar makes with one half of the aluminum bar.
Then, the angle between invar bars and aluminum bar is,
Here,
Rearrange the above equation for
Conclusion:
Therefore, the angle between the invar bars and the aluminum bar as a function of Celsius temperature is
(e)
The greatest attainable angle between the invar bars.
(e)
Answer to Problem 31AP
The greatest attainable angle between the invar bars is
Explanation of Solution
Given info: The distance between two holes drilled at
The average coefficient of linear expansion of the aluminum is
The average coefficient of linear expansion of the invar is
The greatest angle is occur at
The equation for the angel between the invar bars is,
Substitute
Conclusion:
Therefore, the greatest attainable angle between the invar bars is
(f)
The smallest attainable angle between the invar bars.
(f)
Answer to Problem 31AP
The smallest attainable angle between the invar bars is
Explanation of Solution
Given info: The distance between two holes drilled at
The average coefficient of linear expansion of the aluminum is
The average coefficient of linear expansion of the invar is
The smallest angle is occur at
The equation for the angel between the invar bars is,
Substitute
Conclusion:
Therefore, the smallest attainable angle between the invar bars is
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Chapter 18 Solutions
Physics for Scientists and Engineers with Modern Physics
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